Fourier Transforms Of Invariant Functions On Finite Reductive Lie Algebras
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Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
The Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.
Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras
The Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.
Algebraic Groups and Lie Groups with Few Factors
Author: Alfonso Di Bartolo
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-04-17
This volume treats algebraic groups from a group theoretical point of view and compares the results with the analogous issues in the theory of Lie groups. It examines a classification of algebraic groups and Lie groups having only few subgroups.